Choose the correct answer from the given four options. The domain… - Vidyadip

Question

Choose the correct answer from the given four options.

The domain of the function defined by $\text{f}(\text{x})=\sin^{-1}\sqrt{\text{x}-1}$ is:

[1, 2]
[-1, 1]
[0, 1]
none of these.

✓

Answer

[1, 2]

Solution:

$\text{f}(\text{x})=\sin^{-1}\sqrt{\text{x}-1}$

$\Rightarrow\ 0\leq\text{x}-1\leq1$ $[\because\ \sqrt{\text{x}-1}\geq0\ \text{and}\ -1\leq\sqrt{\text{x}-1}\leq1]$

$\Rightarrow\ 1\leq\text{x}\leq2$

$\therefore\ \text{x}\in[1,2]$

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